TS EAMCET · Maths · Probability
If \(X\) is a poisson variate with \(P(X=0)=0.8\), then the variance of \(X\) is
- A \(\log _e 20\)
- B \(\log _{10} 20\)
- C \(\log _e 5 / 4\)
- D \(0\)
Answer & Solution
Correct Answer
(C) \(\log _e 5 / 4\)
Step-by-step Solution
Detailed explanation
Poisson distribution \[ \begin{aligned} & P(X)=\frac{e^{-m} m^x}{x !} \\ & \therefore \quad P(X=0)=\frac{e^{-m} 1}{1} \\ & \Rightarrow \quad 0.8=e^{-m} \Rightarrow-m=\log _e 0.8 \\ & \Rightarrow \quad m=\log _e \frac{10}{8}=\log _e \frac{5}{4} \\ & \end{aligned} \] As, we know…
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